Funky KK hand

[DrPublo]

PP 100NL. Standard opponents.

One limp to me on the CO ($140), and I raise to $5 with KK. Button folds and BB (unremarkable, covers me) reraises to $15. Limper folds and I call.

Flop ($30): 393r.

He bets $25. I figure I'm way ahead or way behind here and just call, intending to call down.

Turn ($80): [3 9 3] A, completing the rainbow

Uh oh.

He bets $20, which is small. He either really liked or really disliked this card. I figure aces full will check, so now I really dont know what to do. I think if I call here he probably won't bet QQ again on the river but probably will bet again with an ace. I call.

River ($120): Brick. [3 9 3] A x

He bets $75, which is exactly what I have left.

I fold with a very dissatisfied taste in my mouth. Fold the turn?

The Doc